The thylacine (Thylacinus cynocephalus), one of Australia's most characteristic megafauna, was the largest marsupial carnivore until hunting, and potentially disease, drove it to extinction in 1936. Although thylacines were restricted to Tasmania for 2 millennia prior to their extinction, recent so‐called plausible sightings on the Cape York Peninsula in northern Queensland have emerged, leading some to speculate the species may have persisted undetected. We compiled a data set that included physical evidence, expert‐validated sightings, and unconfirmed sightings up to the present day and implemented a range of extinction models (focusing on a Bayesian approach that incorporates all 3 types of data by modeling valid and invalid sightings as independent processes) to evaluate the likelihood of the thylacine's persistence. Although the last captive individual died in September 1936, our results suggested that the most likely extinction date would be 1940. Our other extinction models estimated the thylacine's extinction date between 1936 and 1943, and the most optimistic scenario indicated that the species did not persist beyond 1956. The search for the thylacine, much like similar efforts to rediscover other recently extinct charismatic taxa, is likely to be fruitless, especially given that persistence on Tasmania would have been no guarantee the species could reappear in regions that had been unoccupied for millennia. The search for the thylacine may become a rallying point for conservation and wildlife biology and could indirectly help fund and support critical research in understudied areas such as Cape York. However, our results suggest that attempts to rediscover the thylacine will be unsuccessful and that the continued survival of the thylacine is entirely implausible based on most current mathematical theories of extinction.